Battery model parameter identification method based on adaptive forgetting factor least square

Abstract

The invention relates to the technical field of battery model parameter identification, in particular to an adaptive forgetting factor least square-based battery model parameter identification method, which comprises the following steps of: establishing a second-order RC equivalent circuit model of a lithium battery, and determining model parameters to be identified; constructing a relational expression of the open-circuit voltage and the state of charge of the lithium battery; and performing iterative solution on the to-be-identified model parameters by using an improved adaptive forgetting factor least square method, traversing all current and voltage measured values through adaptive adjustment of the improved adaptive forgetting factor, and then terminating iteration. According to the adaptive forgetting factor least square improvement method, the identification precision is improved, the method is simpler, the influence of the undetermined coefficient on the error tracking capability is reduced, and the model parameter identification precision is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of battery model parameter identification, and in particular to a battery model parameter identification method based on adaptive forgetting factor least squares. Background Art

[0002] Power lithium batteries are widely used in electric vehicle energy storage devices due to their high energy density and long cycle life. However, the charging and discharging process of lithium batteries has dynamic nonlinear characteristics, is accompanied by complex electrochemical reactions inside, and is easily affected by external factors, making it difficult to accurately estimate the state of charge (SOC).

[0003] At present, the common SOC estimation model is the second-order RC equivalent circuit model; obtaining high-precision model parameters is the key to establishing the model. The recursive least squares algorithm RLS is a commonly used model parameter identification method. This method is simple and stable, but with the increase of data in the recursive process, the generation of new data will be affected by the old data, resulting in large errors; the least squares method with forgetting factor FFRLS adjusts the ratio of new and old data through the forgetting factor to reduce the proportion of old data. It has the characteristics of high precision and simple structure, but the fixed forgetting factor affects the time-varying and identification accuracy of the parameter identification results; the variable forgetting factor least squares method VFFRLS changes the forgetting factor size in real time by correcting the error; the adaptive forgetting factor least squares method AFFRLS adaptively processes the forgetting factor by correcting the error. Compared with VFFRLS, it has higher accuracy and response speed, but its undetermined coefficient has a larger range of values, which affects the algorithm's ability to track errors. Summary of the invention

[0004] In view of the shortcomings of the existing methods, the present invention designs a simpler adaptive forgetting factor least squares improvement method that improves identification accuracy, reduces the influence of undetermined coefficients on error tracking capability, and improves the identification accuracy of model parameters.

[0005] The technical solution adopted by the present invention is: a battery model parameter identification method based on adaptive forgetting factor least squares includes the following steps:

[0006] Step 1: Establish a second-order RC equivalent circuit model of the lithium battery and determine the model parameters to be identified;

[0007] As a preferred embodiment of the present invention, the model parameters to be identified include: internal resistance, electrochemical polarization resistance, electrochemical polarization capacitance, concentration polarization resistance and concentration polarization capacitance.

[0008] Step 2: Construct an expression for the relationship between the open circuit voltage and the state of charge of the lithium battery;

[0009] As a preferred embodiment of the present invention, the relationship between the open circuit voltage and the state of charge is obtained by using the mixed pulse power characteristic.

[0010] As a preferred embodiment of the present invention, the relationship expression between the open circuit voltage and the state of charge is obtained by fitting an 8th-order curve.

[0011] Step 3, using the improved adaptive forgetting factor least square method to iteratively solve the model parameters to be identified, and the iteration is terminated after traversing all current and voltage measurement values ​​through adaptive adjustment of the improved adaptive forgetting factor;

[0012] As a preferred embodiment of the present invention, step three specifically includes:

[0013] Initialize the forgetting factor λ and the prediction error e base , parameter vector θ0 to be estimated and error covariance P0;

[0014] The amount of data to be input The least squares formula Y(k) is input with the forgetting factor and the least squares method is used to obtain the gain K k and prediction error e(k);

[0015] Update the parameter vector θ(k) to be estimated and the error covariance P(k);

[0016] Input the parameter vector θ(k) to be estimated into the second-order RC equivalent circuit model to obtain the model parameters to be identified;

[0017] The improved forgetting factor expression is used to update the λ(k) value, and the update of the model parameters to be identified is completed after traversing all current and voltage measurement values.

[0018] As a preferred embodiment of the present invention, the formula of the improved forgetting factor expression is:

[0019]

[0020] Among them, λ max is the expected maximum value, λ min is the expected minimum value, e(k) is the prediction error, and e base is the reference error, and n is the power value.

[0021] As a preferred embodiment of the present invention, n is 2 or 4.

[0022] As a preferred embodiment of the present invention, a battery model parameter identification system based on adaptive forgetting factor least squares includes: a memory for storing instructions executable by a processor; a processor for executing instructions to implement a battery model parameter identification method based on adaptive forgetting factor least squares.

[0023] As a preferred embodiment of the present invention, a computer readable medium stores a computer program code, and when the computer program code is executed by a processor, a battery model parameter identification method based on adaptive forgetting factor least squares is implemented.

[0024] Beneficial effects of the present invention:

[0025] 1. Firstly, a second-order RC equivalent circuit model of lithium battery was established, the least squares method of adaptive forgetting factor was improved, and a simpler adaptive update formula of forgetting factor was designed, which reduced the influence of the unknown coefficients on the tracking ability of the algorithm and effectively improved the identification accuracy of model parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 is the second-order RC equivalent circuit model of the lithium battery of the present invention;

[0027] Figure 2 is the OCV-SOC relationship curve of the present invention;

[0028] Figure 3 This is the improved adaptive forgetting factor least squares parameter identification flow chart;

[0029] Figure 4 This is the FUDS test voltage waveform in this example;

[0030] Figure 5 This is the FUDS test current waveform in this example;

[0031] Figure 6 is the ohmic internal resistance R0 identified by the four algorithms in this example;

[0032] Figure 7 is the polarization resistance R1 identified by the four algorithms in this example;

[0033] Figure 8 is the polarization resistance R2 identified by the four algorithms in this example;

[0034] Fig. 9 is the polarized capacitor C1 identified by the four algorithms in this example;

[0035] Fig.10 is the polarized capacitor C2 identified by the four algorithms in this example;

[0036] Fig.11 This is the error diagram between the voltage values ​​of the four algorithm parameter models and the experimentally measured terminal voltage values ​​in this example;

[0037] Fig.12 This is a graph showing changes in the forgetting factor of the improved adaptive forgetting factor least squares method in this example. DETAILED DESCRIPTION

[0038] The present invention is further described below in conjunction with the accompanying drawings and embodiments. This figure is a simplified schematic diagram, which only illustrates the basic structure of the present invention in a schematic manner, and therefore it only shows the components related to the present invention.

[0039] The battery model parameter identification method based on adaptive forgetting factor least squares includes the following steps: Step 1, establish a second-order RC equivalent circuit model of the lithium battery to determine the model parameters to be identified; build Figure 1 The equivalent circuit shown is expressed as follows according to Kirchhoff's law:

[0040]

[0041] Among them, U L is the terminal voltage, U OC is the open circuit voltage OCV, I is the output current, R0 is the internal resistance, R1 and C1 are the electrochemical polarization resistor and electrochemical polarization capacitor respectively, R2 and C2 are the concentration polarization resistor and concentration polarization capacitor respectively, and U1 and U2 are the voltages across R1, C1 and R2, C2 respectively.

[0042] Performing Laplace transform on equation (1) yields:

[0043]

[0044] Let the time constant τ1=R1C1, τ2=R2C2, simplifying to get:

[0045]

[0046] Assume the discretized form is:

[0047]

[0048] Among them, a0, a1, a2, a3, and a4 are constants.

[0049] Let Y(k) = U OC (k)-U L (k), then combined with formula (4), we can get:

[0050] Y(k)=a0Y(k-1)+a1Y(k-2)+a2I(k)+a3I(k-1)+a4I(k-2) (5)

[0051] Then the parameter relationship of the second-order RC equivalent circuit model is a least squares formula, which can be expressed as:

[0052] Y(k)=φ T (k)θ(k) (6)

[0053] The input data volume Parameter vector to be estimated θ(k) = [a0 a1 a2 a3 a4] T , the system output is Y(k).

[0054] Will Substituting into formula (4) and comparing with formula (3), we can get:

[0055]

[0056] Among them, the intermediate variables k1=R0, k2=R0τ1+R0τ2+R1τ2+R2τ1, k3=R0+R1+R2, and T' is the sampling time.

[0057] The parameter expression of the second-order RC equivalent circuit model is obtained from formula (7):

[0058]

[0059] That is, the model parameters to be identified are R0, R1, C1, R2, and C2.

[0060] Step 2: Determine the relationship between the open circuit voltage OCV and the state of charge SOC of the lithium battery;

[0061] The relationship between open circuit voltage (OCV) and state of charge (SOC) is obtained by using hybrid pulse power characterization (HPPC).

[0062] HPPC tests the battery in the following steps:

[0063] First, the battery was fully charged and left to stand for 2 hours; then, it was discharged 10% SOC and left to stand for 2 hours until the battery was discharged; the battery terminal voltage measured after each standing was the OCV value corresponding to the SOC point; the above test was repeated 3 times, and then the collected data were averaged. The averaged SOC and OCV data are shown in Table 1.

[0064] Table 1 SOC and OCV data

[0065]

[0066] Matlab was used to perform 8th-order curve fitting on SOC and OCV data to obtain the OCV-SOC relationship curve, as shown in Figure 2 As shown, the fitted function relationship is as follows

[0067]

[0068] Through the OCV-SOC relationship curve, OCV (UOC ), and then Y(k)=U OC (k)-U L (k) to get Y(k), U L (k) and I are both known battery voltage and current data. The battery SOC can be obtained by integrating the current with respect to time (ampere-hour integration method).

[0069] like Figure 3 As shown, step three, iteratively solve based on the improved adaptive forgetting factor least square method, and adaptively adjust the forgetting factor;

[0070] The expression of recursive least squares method is as follows:

[0071]

[0072] Among them, K k For gain, is the estimated value at time k, P(k) is the error covariance at time k, and I' is the unit matrix.

[0073] The least squares method with forgetting factor introduces the forgetting factor λ to reduce the proportion of old data and improve the correction effect of new data. Its expression is:

[0074]

[0075] Among them, e(k) is the prediction error, and the value range of λ is generally 0.9-1.

[0076] Formula (12) is the existing adaptive forgetting factor least squares method. When e(k) is greater than the prediction allowable error, the λ value approaches the expected minimum value λ min ; Correspondingly, when it is less than the prediction allowable error, the λ value becomes larger, and the λ value update expression is

[0077]

[0078] Among them, e base is the allowable error, round(·) is the rounding function, and h is the sensitivity coefficient, which can change the sensitivity of the λ value to the error and takes a value between 0 and 1. When h is close to 1, the λ value changes slowly. Conversely, the closer h is to 0, the faster the λ value changes.

[0079] The improved adaptive forgetting factor least square method of the present invention avoids the influence of the value of the undetermined coefficient h on the algorithm tracking ability; at the same time, when e(k) is large, the λ value can quickly approach the minimum value, and when e(k) is within the error allowable range, the λ value can quickly approach the maximum value. The update expression of the improved forgetting factor λ is:

[0080]

[0081] Among them, λ max is the expected maximum value, λ min is the expected minimum value.

[0082] The λ value is limited between the maximum and minimum values ​​by formula (13), e base is the prediction allowable error, when e(k) <e base When the ratio is magnified by the nth power, n is 2 or 4, and λ quickly approaches λ max ;When e(k)>e base When , the ratio will be further reduced, making λ quickly approach λ min。

[0083] Figure 3 First, initialize the forgetting factor λ = 1 and the prediction error e base = 0.001, parameter vector to be estimated θ0 = [0 0 0 0 0] T , Error covariance P0 = 10 4 ×eye(5,5);

[0084] The amount of input data Combine formula (11) and formula (6) to calculate the gain K k , prediction error e(k);

[0085] Update the parameter vector θ(k) to be estimated and the error covariance P(k);

[0086] The parameter vector θ(k) to be estimated is calculated by formula (7) and formula (8) to obtain the model parameters to be identified;

[0087] Then, the λ(k) value is adaptively updated by formula (13); it is determined whether all current and voltage measurement values ​​have been traversed;

[0088] If the traversal is completed, the update of the model parameters to be identified is terminated, and the value of the parameter vector θ(k) to be estimated is output; otherwise, k=k+1, and the execution is returned to continue.

[0089] To illustrate the effect of the method of this embodiment, a ternary lithium battery with a rated voltage of 3.6V and a capacity of 2Ah is selected for experimental verification; the battery is subjected to a Federal Urban Driving Schedule (FUDS) test, and the voltage and current waveforms during the test are as follows: Figure 4 and Figure 5As shown in the figure, the battery management system is used to collect the voltage and current data of the battery, and then the method proposed in this example is applied and compared with the adaptive forgetting factor least squares method (AFFRLS), the variable forgetting factor least squares method (VFFRLS) and the recursive least squares method (RLS) to verify the accuracy of the parameter identification results of the four algorithms.

[0090] The output voltage value of the second-order RC equivalent circuit model at the corresponding moment is obtained by the identified parameters at each moment and the input current value at the corresponding moment. The output voltage value of the parameter model is compared with the terminal voltage value measured experimentally to evaluate the accuracy of the parameter identification algorithm.

[0091] In order to more directly compare the recognition accuracy of the four algorithms, the error evaluation index in formula (14) is used for analysis.

[0092]

[0093] Where, MAE is the mean absolute error; RMSE is the root mean square error; U L (k) is the terminal voltage value measured experimentally at time k; is the output voltage value of the parameter model at time k.

[0094] Under FUDS working condition, the ohmic internal resistance R0, polarization resistance R1, polarization resistance R2, polarization capacitance C1 and polarization capacitance C2 identified by the four algorithms are as follows: Figure 6-Figure 10 shown; combined Figure 5 The current changes in the 5 graphs show that the RLS graph has the most gentle trend, the smallest graph fluctuation, and the worst parameter dynamic characteristics, followed by the VFFRLS and AFFRLS graphs. The parameters of the present invention can track the current changes in a timely manner, and the parameter dynamic characteristics are the best. The difference between the output voltage value of the parameter model and the terminal voltage value measured experimentally is shown in Fig.11 As shown, the forgetting factor changes as Fig.12 As shown in the figure, the forgetting factor can be continuously and adaptively adjusted according to the change of voltage error.

[0095] From the identification results, the parameters identified by the improved adaptive forgetting factor least squares method of the present invention have better tracking ability for the changes of current and voltage, and have better parameter identification accuracy under the condition of drastic changes in voltage and current; Fig.11 It can be seen that the error between the voltage value of the parameter model identified by the improved adaptive forgetting factor least square method of the present invention and the voltage value measured experimentally is the smallest. Table 2 shows the results of the four algorithms on the two error indicators of MAE and RMSE.

[0096] Table 2 Errors of four algorithms under FUDS

[0097]

[0098] It can be seen from Table 2 that compared with AFFRLS, VFFRLS and RLS algorithms, the algorithm of the present invention reduces MAE by 0.02794mV, 0.05349mV and 0.08498mV respectively, and the corresponding accuracy is improved by 6.02%, 10.93% and 16.31% respectively; in terms of RMSE, the algorithm of the present invention also reduces RMSE by 0.01543mV, 0.03103mV and 0.04658mV respectively compared with AFFRLS, VFFRLS and RLS algorithms.

[0099] The present invention improves the adaptive forgetting factor least squares method and designs a simpler forgetting factor adaptive updating formula, thereby avoiding the influence of the value of the undetermined coefficient on the algorithm tracking ability. Through experimental data and algorithm simulation, it is verified that the improved adaptive forgetting factor least squares method has good tracking ability and high accuracy in lithium battery model parameter identification.

[0100] Based on the above ideal embodiments of the present invention, the relevant staff can make various changes and modifications without departing from the technical concept of the present invention through the above description. The technical scope of the present invention is not limited to the contents of the specification, and its technical scope must be determined according to the scope of the claims.

Claims

1. A battery model parameter identification method based on adaptive forgetting factor least squares, characterized in that: The following steps are involved: Step 1: Establish a second-order RC equivalent circuit model of the lithium battery and determine the model parameters to be identified; Step 2: Construct an expression for the relationship between the open circuit voltage and the state of charge of the lithium battery; Step 3: Use the improved adaptive forgetting factor least square method to iteratively solve the model parameters to be identified. Through the adaptive adjustment of the improved adaptive forgetting factor, the iteration is terminated after traversing all current and voltage measurement values.

2. The battery model parameter identification method based on adaptive forgetting factor least squares according to claim 1 is characterized in that: Step three specifically includes: Initialize the forgetting factor λ and the prediction error e base , parameter vector θ0 to be estimated and error covariance P0; The amount of data to be input The least squares formula Y(k) is input with the forgetting factor and the least squares method is used to obtain the gain K k and prediction error e(k); Update the parameter vector θ(k) to be estimated and the error covariance P(k); Input the parameter vector θ(k) to be estimated into the second-order RC equivalent circuit model to obtain the model parameters to be identified; The improved forgetting factor expression is used to update the λ(k) value, and the update of the model parameters to be identified is completed after traversing all current and voltage measurement values.

3. The battery model parameter identification method based on adaptive forgetting factor least squares according to claim 2 is characterized in that: The formula of the improved forgetting factor expression is: Among them, λ max is the expected maximum value, λ min is the expected minimum value, e(k) is the prediction error, and e base is the reference error, and n is the power value.

4. The battery model parameter identification method based on adaptive forgetting factor least squares according to claim 3 is characterized in that: n is 2 or 4.

5. The battery model parameter identification method based on adaptive forgetting factor least squares according to claim 1, characterized in that: The model parameters to be identified include: internal resistance, electrochemical polarization resistance, electrochemical polarization capacitance, concentration polarization resistance and concentration polarization capacitance.

6. The battery model parameter identification method based on adaptive forgetting factor least squares according to claim 1, characterized in that: The relationship between open circuit voltage and state of charge is obtained using hybrid pulse power characteristics.

7. The battery model parameter identification method based on adaptive forgetting factor least squares according to claim 6 is characterized in that: The relationship between open circuit voltage and state of charge is obtained by 8th-order curve fitting.

8. The battery model parameter identification system based on adaptive forgetting factor least squares is characterized by: include: a memory for storing instructions executable by a processor; A processor, configured to execute instructions to implement the battery model parameter identification method based on adaptive forgetting factor least squares as described in any one of claims 1 to 7.

9. A computer readable medium storing a computer program code, characterized in that: When the computer program code is executed by a processor, the method for identifying battery model parameters based on adaptive forgetting factor least squares as described in any one of claims 1 to 7 is implemented.

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